Tutorial Review of Mixing in a Rotating Soft Microchannel under Electrical Double Layer Effect: A Variational Calculus Approach

Abstract

We study the effect of the grafted polyelectrolyte layer on the flow dynamics, and its consequences on underlying mixing in the rotating microfluidic channel. For this analysis, the method used by Sadeghi et al. (J. Fluid Mech., vol. 887, 2020, pp. A13; Phys. Rev. Fluids., vol. 4 (6), 2019, 063701-23), is modified by incorporating the non-linear effect stemming from the polyelectrolyte layer induced electrostatics to solve the coupled system of equations, integrated with the non-homogeneous boundary conditions. This method is used to obtain the velocity distribution in the asymptotic limit of geostrophic plug flow under the framework of variational calculus approach. We analyze the mixing dynamics from the perspective of both qualitative assessment and quantitative evaluation. For the qualitative estimation, we focus on the Poincaré map analysis, while the entropy of mixing approach is used for the mixing quantification. Results show that the grafted polyelectrolyte layer in contact with the ionic solution leads to the development of an electrical double layer, which upon interacting with the external electric field, strengthens the electroosmotic pumping in the fluidic channel. Such polyelectrolyte layer modulated strong electroosmotic pumping together with its intrinsic feature of offering a frictional drag to the underlying transport helps to modulate the primary as well as the secondary flows in the channel under the influence of rotational forces. With an alteration in the electroosmotic pumping and frictional drag force, tuneable through the thickness of the grafted polyelectrolyte layer, we obtain different types of secondary flow vortex configurations viz., a standard double-vortex, dumbbell-shaped vortex and the transition state between the formers. A significant change in the structure and strengths of these vortices modulates the chaotic mixing in the present configuration